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Finding the Third Proportional to 2,009 and 2,288

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Solution

The third proportional to 2,009 and 2,288 is: 2,605.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,009 : 2,288 = 2,288 : x
  2. Step 2: Convert to fraction form
    2,009/2,288 = 2,288/x
  3. Step 3: Cross multiply
    2,009x = 2,288 × 2,288
  4. Step 4: Simplify right side
    2,009x = 5,234,944
  5. Step 5: Solve for x
    x = 5,234,944/2,009
  6. Step 6: Final answer
    x = 2,605.75

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.